Executable Behaviour and the \pi-Calculus (extended abstract)

TL;DR

This paper explores the relationship between executable behaviors modeled by reactive Turing machines and their specification in the pi-calculus, establishing that all executable behaviors can be represented in the pi-calculus up to divergence-preserving branching bisimilarity, but not vice versa.

Contribution

It demonstrates that the pi-calculus can specify all executable behaviors of reactive Turing machines up to divergence-preserving branching bisimilarity, and proposes a restriction to align pi-calculus specifications with executability.

Findings

All executable behaviors can be specified in the pi-calculus up to divergence-preserving branching bisimilarity.

The pi-calculus can specify behaviors not executable by reactive Turing machines.

A restricted version of the pi-calculus aligns with executable behaviors up to divergence bisimilarity.

Abstract

Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the pi-calculus. We establish that all executable behaviour can be specified in the pi-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended) limitations of the model of reactive Turing machines. That is, the pi-calculus allows the specification of behaviour that is not executable up to divergence-preserving branching bisimilarity. Motivated by an intuitive understanding of executability, we then consider a restriction on the operational semantics of the pi-calculus that does associate with every pi-term executable behaviour, at least up to the version of branching bisimilarity that does not require the preservation of divergence.